Abstract:
Based on the mathematical model for dynamics of a saturated poroelastic Timoshenko beam, the dynamical behavior of a simply-supported saturated poroelastic Timoshenko beam, with two permeable ends and subjected to a sudden step load at its midpoint, is investigated. The analytical solution is obtained, and the variations of the dimensionless deflections, bending moments of the solid skeleton of the poroelastic beam, and equivalent couples of the pore fluid pressure against the dimensionless time are given. The effects of the shearing and rotation inertia of the cross section on the dynamical behavior are examined, and the dynamical behaviors of the saturated poroelastic Timoshenko, Shear, Rayleigh and Euler-Bernoulli beams are compared. It is shown that the shearing effect increases the amplitudes and periods of the dynamical responses of the saturated poroelastic Timoshenko beam, while the rotation inertia effect of the cross section only increases the periods. The interaction between the solid skeleton and pore fluid plays a role as viscidity. With the interaction coefficient increasing, the deflections and bending moments of the saturated poroelastic beam decrease, and the amplitudes of the equivalent couple of the pore fluid pressure increase, furthermore, the attenuation of the vibration amplitudes is more rapidly with the increasing of the interaction coefficient. Meanwhile, with the slenderness ratio increasing, the amplitude and period of the saturated poroelastic Timoshenko beam decrease gradually, and they converge to those of the saturated poroelastic Euler-Bernoulli beam.